In　reality,　the　behavior　and　nature　of　nonlinear　dynamical　systems　are　ubiquitous　in　many　practical　engineering　problems.　The　mathematical　models　of　such　problems　are　often　governed　by　a　set　of　coupled　second-order　differential　equations　to　form　multi-degree-of-freedom　(MDOF)　nonlinear　dynamical　systems.　It　is　extremely　difficult　to　find　the　exact　and　analytical　solutions　in　general.　In　this　paper,　the　homotopy　analysis　method　is　presented　to　derive　the　analytical　approximation　solutions　for　MDOF　dynamical　systems.　Four　illustrative　examples　are　used　to　show　the　validity　and　accuracy　of　the　homotopy　analysis　and　modified　homotopy　analysis　methods　in　solving　MDOF　dynamical　systems.　Comparisons　are　conducted　between　the　analytical　approximation　and　exact　solutions.　The　results　demonstrate　that　the　HAM　is　an　effective　and　robust　technique　for　linear　and　nonlinear　MDOF　dynamical　systems.　The　proof　of　convergence　theorems　for　the　present　method　is　elucidated　as　well.　Copyright　©　2010　by　ASME.